# Representation, Bandwidth and composition of Digital Signals

I have started learning data communication and I'm not able to grasp certain topics.

First

(i) I know that analog signals are continuous and digital signals are discrete. Analog signal are represented by a continuous time-varying quantity like voltage. How are digital signals represented in actual practice? I mean to ask how are the 0s & 1s actually represented/transmitted over a transmission medium? Are they represented by a sudden spike then staying stable and then a sudden fall of the time-varying quantity like voltage?

Second,

(i) I know bandwidth is the range of frequencies that make up a composite analog signal. So, if there are two analog signal with frequency 5 Hz and 10 Hz making up a composite signal, will it's bandwidth be (10-5=) 5 hz?

(ii) When we say bandwidth of a transmission medium is 5 hertz, do we mean to say that it allows any composite signal to pass through it, in which difference between the upper frequency and lower frequency making up the composite signal is 5 Hz?

(iii) Can we define bandwidth of a single sine analog signal?

Third

(i) Are digital signal nothing but just superimposition of theoretically an infinite number of analog signals? If yes, then why and how?

(ii) How do we define frequency and bandwidth(in Hertz, not bps) of a digital signal?

Sorry if these questions seem a bit too easy for many but as a self-learner with no college help, It's quite tough for me. Thanks in advance.

First

(i) I know that analog signals are continuous and digital signals are discrete. Analog signal are represented by a continuous time-varying quantity like voltage. How are digital signals represented in actual practice? I mean to ask how are the 0s & 1s actually represented/transmitted over a transmission medium? Are they represented by a sudden spike then staying stable and then a sudden fall of the time-varying quantity like voltage?

Physical representation of discrete-time (or digital) signals is also through analog waveforms, but the information they carry is discrete. They can be transmitted like pulses of $$5$$ V, $$0$$ V in a digital computer, or sine waves of different frequencies like in a digital telephone line.

Second,

(i) I know bandwidth is the range of frequencies that make up a composite analog signal. So, if there are two analog signal with frequency 5 Hz and 10 Hz making up a composite signal, will it's bandwidth be (10-5=) 5 hz?

If you include all frequencies from $$0$$ Hz upto the max in the signal, then the bandwidth of your composite baseband signal will be $$10-0 = 10$$ Hz., counting only the positive excursion of frequencies. If you want to consider your signal as bandpass then its bandwidth will be $$10-5=5$$ Hz.

(ii) When we say bandwidth of a transmission medium is 5 hertz, do we mean to say that it allows any composite signal to pass through it, in which difference between the upper frequency and lower frequency making up the composite signal is 5 Hz?

No. The actual frequency range of that passband is also important; a medium that can transmit a band in [15-20] Hz cannot transmit a signal in the band [85-90] Hz, even though both have the same bandwidth. You should shift the signal spectrum into the channel band for transmission.

(iii) Can we define bandwidth of a single sine analog signal?

Bandwidth of $$x(t)=\cos(2 \pi f_0 t)$$ is its frequency $$f_0$$ if you treat it like a baseband signal, but otherwise $$0$$ Hz if you treat it like bandpass signal...

Third

(i) Are digital signal nothing but just superimposition of theoretically an infinite number of analog signals? If yes, then why and how?

digital signal is a misnomer here. It's true that an ideal pulse waveform requires infinite spectrum and infinite number of sine waves to construct it, but a pulse is not the only way to carry digital information as the answer to the first question already indicated...

(ii) How do we define frequency and bandwidth(in Hertz, not bps) of a digital signal?

digital signal is a misnomer here, it's the discrete information that you actually should care, that information is quantified by an entropy measure. Then this will be transmitted via line signalling with analog bandwidth in Hz depending on the efficiency of signalling waveforms.